the problem with long term rentals on this island is that there are some people that take advantage of the french laws pertaining to the rights of a renter. I know several owners who got screwed by people moving in and then not paying, and it takes a long time to get renters out of your property in france regardless if they pay or not.
my guess this is the main reason its difficult to find a year round rental property. a lot of long term rentals on the island are guaranteed by a business, then it is safer to rent long term.